Question

Given tan θ = 3/4 for acute angle θ, find the value of a and b for the statement cos θ = a/b.

Answer 1

Explanation:

`\tan \theta = (3)/(4) \\ \\ \sec \theta = \sqrt{1 + { \tan }^(2) \theta} \\ \hspace{22 pt} = \sqrt{1 + {( (3)/(4) )}^(2) } \\ \hspace{22 pt} = \sqrt{1 + {(9)/(16) }} \\ \hspace{22 pt} = \sqrt{ {(16 + 9)/(16) }} \\ \hspace{22 pt} = \sqrt{ {(25)/(16) }} \\ \red{ \boxed{\bold{ \therefore \sec \theta = { {(5)/(4) }} }}} \\ \\ \cos \theta = (1)/(\sec \theta ) = (4)/(5) = (a)/(b) \\ \\ \implies \: a = 4 \: and \: b = 5`